I would bet that the lowest power consumption would be either the nano-itx mobo or the EPIA-5000 fanless mobo. You could equip either with a USB flash or compact flash. You could use the ultra compact power supply driven by a 12 volt solar panel. The dc-dc power supply consumes very little leaving the board as the significant consumer.

To be conservative your solar panel should be able to provide around 20 watts of power at 12 volts.

Via has just announced a new EK series of boards. One runs at 800 Mhz and consumes only 19 watts. (It is also fanless)